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SUMMARY:Multicentric calculus: polynomial as a new variable - Olavi Nevanl
 inna (Aalto University)
DTSTART:20141113T150000Z
DTEND:20141113T160000Z
UID:TALK56156@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:We outline some ideas on multicentric calculus.\n\nThe basic t
 echnical tool is to change variable z to w as follows:\n\n                
      w = p(z).\n\nHere p is a polynomial in the complex plane (or real lin
 e) with simple roots. Since this is a many-to-one mapping\, we compensate 
 the "loss of information" by introducing a vector valued function f to rep
 resent the original scalar function φ. We call the approach as "multicent
 ric calculus".\n\nMulticentric calculus can be used in an effective way to
  compute φ(A) when p(A) is much "nicer" than A\, in particular\, when an 
 effective functional calculus exists for p(A) but is not directly availabl
 e for A.\nWe discuss two directions\, one based on holomorphic functional 
 calculus. The other direction then generalizes the simple calculus where c
 ontinuous functions are evaluated at diagonalizable matrices as follows:\n
 \n                           φ(A) = Tφ(D)T−1.\n\nIn particular\, one n
 eed not assume that φ is differentiable if the matrix A has nontrivial Jo
 rdan blocks. This is so far unpublished.
LOCATION:MR 14\, CMS
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